250 



Fishery Bulletin 104(2) 



The trawl used in the DMR survey is similar in de- 

 sign, but smaller than that used in NMFS, although the 

 size of the mesh liner in the codend is the same. The 

 DMR survey trawl net is also towed for less time (20 

 minutes versus 30 minutes for NMFS). 



The data collected in the inshore survey were ana- 

 lyzed according to the methods described below. The 

 stratified mean number of lobsters per tow, X. can be 

 calculated as 



The stratified mean number of lobsters of length j per 

 tow, X,, can be estimated as 





where the mean number of lobsters of size j per tow, 

 X I,, is estimated as 



where g = the number of stratum in the survey; 

 A^ = the survey area in stratum k\ ^ 



A = the total area covered by the survey (A='^A^ ); 

 and *=' 



Xj. = the average catch per tow in stratum k. 



The X, can be calculated as 



X 



IkX 



.iJ.k 



l.k - 



The above equations were used for both the original 

 data (without any transformation) and the data trans- 

 formed by using log(.r-i-l). For results derived from the 

 log (.t+l) transformed data, a retransformation was done 

 to retransform the log-based results to the results of the 

 original scale by using the following equation: 



X, 



-tX,.n 



'k /=1 



where X/, , = catch in tow t, stratum k; and 



T,, = the total number of tow in stratum K. 



The variance for the stratified mean, S'-(X), can be esti- 

 mated as 



S~{X) = ^J^A;S'{X,J, 

 A~ i=i 



where S.,(^,,) = the variance for the mean number per 

 tow in stratum k, which can be estimated as 



S2(X, ) = -'=! - 



l<x,,-x,f 



riiAnj. -1) 

 The mean length of the lobster population is estimated 



The average length fish per tow, C,,, in the above equa- 

 tion is calculated as 



C, 



T,. 200 



where L = the lobster carapace size ranging from 1 to 

 200; and 

 X,,,= the number of the lobsters in size /, tow /, 

 and stratum k. 



t/ = exp(y + cTf, /2), 



where Y = the statistics derived from log(.v-i-l) trans- 

 formed data; 

 [/ = is the re-transformed statistics; and 

 o\, = the population variance estimates as 



\Sl+A, 





where Sy and Y/. = the variance and mean value of 

 log(j:-i-l) transformed data in stratum k, respectively. 



Using the above equations, we estimated the strati- 

 fied mean number of lobsters per tow for original and 

 log(.r-i-l) transformed data, the stratified mean size fre- 

 quency, and the stratified mean size of lobsters for the 

 Maine inshore surveys. The average weight of lobsters 

 for each tow was also calculated and then plotted against 

 the average depth of the tow to identify if there was any 

 size-depth dependent distribution. It should be noted 

 that observations of zero lobsters occurred only for a 

 small number of tows in the years covered in our study. 

 Thus for the DMR inshore survey, there was no need to 

 use methods such as delta transformation, which is often 

 used in dealing with zero-inflated survey data with a 

 large number of zero lobster catches. 



The stratified mean number of lobsters per tow, strat- 

 ified mean size frequency, and stratified mean size of 

 lobsters for the NMFS survey program were obtained 

 from the NMFS (Idoine-). Because of the large number 



2 Idoine, J. 2004. Personal comniun. Northeast Fisheries 

 Science Center, 166 Water Street, Woods Hole, MA 02543- 

 1026. 



